Abstract
The stability of five-dimensional (5D) brane-world models under conformal perturbations is investigated. The analysis is carried out in the general case and then it is applied to particular solutions. It is shown that models with the Poincar\'e and de Sitter branes are unstable because they have a negative mass squared of gravexcitons whereas models with the anti--de Sitter branes have a positive gravexciton mass squared and are stable. It is also shown that 4D effective cosmological and gravitational constants on branes as well as gravexciton masses undergo a hierarchy: they have different values on different branes.
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